A new method for solving branching problems in surface reconstruction

The 3D shape reconstruction of an object from its 2D cross-sections is important for reproducing it by NC machining or rapid prototyping. Although several different reconstruction methods have been proposed, most of them have allowed only simple branching, or have had difficulty in handling complex branching structures. In this paper, a new method is presented for solving branching problems in surface reconstruction from a set of free-form contours in planar cross-sections. In this method, we decompose each multiple branching region into a set of single branching regions by providing a set of intermediary contours using modified distance maps. Then, each pair of contours in the single branching regions is linked with triangular facets to construct a piecewise triangular G(1) Bezier surface. An experimental result is given to show that our method gives reasonably good solutions for the representation of complex-shaped objects from planar contours.